How to Divide Square Roots

Step-by-Step Guide

1. 1

   Step 1: Set up a fraction.

   If your expression is not already set up like a fraction, rewrite it this way.
   
   This makes it easier to follow all the necessary steps when dividing by a square root.
   
   Remember that a fraction bar is also a division bar.For example, if you are calculating 144÷36{\displaystyle {\sqrt {144}}\div {\sqrt {36}}}, rewrite the problem like this: 14436{\displaystyle {\frac {\sqrt {144}}{\sqrt {36}}}}.
2. 2

   Step 2: Use one radical sign.

   If your problem has a square root in the numerator and denominator, you can place both radicands under one radical sign.(A radicand is a number under a radical, or square root, sign.) This will simplify the simplifying process.
   
   For example, 14436{\displaystyle {\frac {\sqrt {144}}{\sqrt {36}}}} can be rewritten as 14436{\displaystyle {\sqrt {\frac {144}{36}}}}. , Divide the numbers as you would any whole number.
   
   Make sure to place their quotient under a new radical sign.
   
   For example, 14436=4{\displaystyle {\frac {144}{36}}=4}, so 14436=4{\displaystyle {\sqrt {\frac {144}{36}}}={\sqrt {4}}}. , If the radicand is a perfect square, or if one of its factors is a perfect square, you need to simplify the expression.
   
   A perfect square is the product of a whole number multiplied by itself.For example, 25 is a perfect square, since 5×5=25{\displaystyle 5\times 5=25}.
   
   For example, 4 is a perfect square, since 2×2=4{\displaystyle 2\times 2=4}.
   
   Thus:4{\displaystyle {\sqrt {4}}}=2×2{\displaystyle ={\sqrt {2\times 2}}}=2{\displaystyle =2}So, 14436=4=2{\displaystyle {\frac {\sqrt {144}}{\sqrt {36}}}={\sqrt {4}}=2}.
3. 3

   Step 3: Divide the radicands.

4. 4

   Step 4: Simplify

5. 5

   Step 5: if necessary.

Detailed Guide

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